Question: The common ratio in a geometric series is $0.5$ and the first term is $256$. Find the sum of the first $6$ terms in the series.
This formula gives the sum ${S_n}$ of the first $ n$ terms in the geometric series where the first term is $ a$ and the common ratio is $C r$ : ${S_n}=\dfrac{ a(1-C r^{ n})}{1-C r}$ We are given the values for $ n$, $ a$, and $C r$. All we need to do is plug them in the formula. We are given that ${n=6}$, ${a=256}$, and $C{r=0.5}$ : ${S_n}=\dfrac{{256}(1-(C{0.5})^{{6}})}{1-C{0.5}}$ Evaluating the expression in the calculator, we get that $S_n=504$. In conclusion, the sum of the first $6$ terms in the series is $504$.